The Apparent Trade-Off and Its Disappearance

When these findings were published, they suggested that policy makers faced a trade-off between inflation and unemployment. If they were willing to accept more inflation, they could achieve lower unemployment. This looked like an attractive trade-off, and starting in the early 1960s, U.S. macroeconomic policy aimed at steadily decreasing unemployment. Figure 8-2 plots the combinations of the inflation rate and the unem-ployment rate in the United States for each year from 1961 to 1969. Note how well the relation between unemployment and inflation corresponding to equation (8.4) held during the long economic expansion that lasted throughout most of the 1960s. From 1961 to 1969, the unemployment rate declined steadily from 6.8 to 3.4%, and the inflation rate steadily increased, from 1.0 to 5.5%. Put informally, the U.S. economy moved up along the original Phillips curve. It indeed appeared that, if policy makers were willing to accept higher inflation, they could achieve lower unemployment.

Decrease in uS Increase in p.c

Around 1970, however, the relation between the inflation rate and the unemploy-ment rate, so visible in Figure 8-2, broke down. Figure 8-3 shows the combination of the inflation rate and the unemployment rate in the United States for each year from 1970 to today. The points are scattered in a roughly symmetric cloud. There is no longer any visible relation between the unemployment rate and the inflation rate.

Why did the original Phillips curve vanish? Because wage setters changed the way they formed their expectations about inflation.

This change came, in turn, from a change in the behavior of inflation. The rate of inflation became more persistent. High inflation in one year became more likely to be followed by high inflation the next year. As a result, people, when forming expectations, started to take into account the persistence of inflation. In turn, this change in expectation formation changed the nature of the relation between unemployment and inflation.

MyEconLab

1969

Inflation rate (percent)

8 7 6 5 4 3 2 1 0 –1

3.0 4.0 5.0 6.0 7.0

1968

1967 1966

1965

1964 19621963

1961

Figure 8-2

Inflation versus Unemployment in the United States, 1948–1969 The steady decline in the U.S.

unemployment rate through-out the 1960s was associated with a steady increase in the inflation rate.

Source: Series UNRATE, CPIAUSCL Federal Reserve Economic Data (FRED) http://research.stlouisfed.

org/fred2/.

MyEconLab

–2 0 2 4 6 8 10 12 14

3 4 5 6 7 8 9 10

Inflation (percent)

Unemployment rate (percent)

Figure 8-3

Inflation versus Unemployment in the United States, 1970–2014 Beginning in 1970 in the United States, the relation between the unemployment rate and the inflation rate disappeared.

Source: Series UNRATE, CPIAUSCL Federal Reserve Economic Data (FRED).

MyEconLab

MyEconLab

Let’s look at the argument in the previous paragraph more closely. Suppose expecta-tions of inflation are formed according to:

p_t^e = 11 - u2pQ + upt- 1 (8.5)

In words: Expected inflation this year depends partly on a constant value, pQ, with weight, 1 - u, and partly on inflation last year, which we denote by pt- 1, with weight, u.

The higher the value of u, the more last year’s inflation leads workers and firms to revise their expectations of what inflation will be this year, and so the higher is the expected inflation rate.

We can then think of what happened in the 1970s as an increase in the value of u over time:

■

■ So long as inflation was not persistent, it was reasonable for workers and firms to just ignore past inflation and to assume a constant value for inflation. For the period that Phillips and Samuelson and Solow had looked at, u was close to zero, and expectations were roughly given by p^e = pQ. The Phillips curve was given by equation (8.4).

■

■ But as inflation became more persistent, workers and firms started changing the way they formed expectations. They started assuming that, if inflation had been high last year, inflation was likely to be high this year as well. The parameter u, the effect of last year’s inflation rate on this year’s expected inflation rate, increased.

The evidence suggests that, by the mid-1970s, people expected this year’s inflation rate to be the same as last year’s inflation rate—in other words, that u was now equal to 1.

Now turn to the implications of different values of u for the relation between inflation and unemployment. To do so, substitute equation (8.5) for the value of p_t^e into equation (8.2):

p_t = 11 - u2pQ + upt- 1 + 1m + z2 - aut

■

■ When u equals zero, we get the original Phillips curve, a relation between the inflation rate and the unemployment rate:

p_t = pQ + 1m + z2 - aut

■

■ When u is positive, the inflation rate depends not only on the unemployment rate but also on last year’s inflation rate:

p_t = [11 - u2pQ + 1m + z2] + upt- 1 - aut

■

■ When u equals 1, the relation becomes (moving last year’s inflation rate to the left side of the equation)

p_t - pt- 1 = 1m + z2 - aut (8.6)

So, when u = 1, the unemployment rate affects not the inflation rate, but rather the change in the inflation rate. High unemployment leads to decreasing inflation; low unem-ployment leads to increasing inflation.

This discussion is the key to what happened after 1970. As u increased from 0 to 1, the simple relation between the unemployment rate and the inflation rate disappeared. This disappearance is what we saw in Figure 8-3. But a new relation emerged, this time between the unemployment rate and the change in the inflation rate, as predicted by equation (8.5). This relation is shown in Figure 8-4, which plots the change in the inflation rate versus the unemployment rate observed for each year since 1970, and shows a clear negative relation between the change in inflation and unemployment.

p^e 6

y 5 20.5x 1 3%

–5 –4 –3 –2 –1 0 1 2 3 4 5 6

4.0 5.0 6.0 7.0 8.0 9.0 10.0

Inflation (percentage points)

Unemployment rate (percentage points)

Figure 8-4

Change in Inflation versus Unemployment in the United States, 1970–2014

Since 1970, there has been a negative relation between the unemployment rate and the change in the inflation rate in the United States.

Series CPIAUCSL, UNRATE: Federal Reserve Economic Data (FRED) http://research.stlouisfed.org/fred2/.

MyEconLab

MyEconLab

The line that best fits the scatter of points for the period 1970–2014 is given by

p_t - pt- 1 = 3.0% - 0.5ut (8.7)

The line is drawn in Figure 8-4. For low unemployment, the change in inflation is positive. For high unemployment, the change in inflation is negative. To distinguish it from the original Phillips curve (equation (8.4)), equation (8.6)—or its empirical counter-part, equation (8.7)—is often called the modified Phillips curve, or the expectations-augmented Phillips curve (to indicate that p_{t- 1} stands for expected inflation), or the accelerationist Phillips curve (to indicate that a low unemployment rate leads to an increase in the inflation rate and thus an acceleration of the price level). We shall simply call equation (8.7) the Phillips curve and refer to the previous incarnation, equation (8.4), as the original Phillips curve.

Before we move on, one last observation. Although there is a clear negative rela-tion between unemployment and the change in the inflarela-tion rate, you can see that the relation is far from tight. Some points are far from the regression line. The Phillips curve is both a crucial and a complex economic relation. It comes with plenty of warn-ings, which we shall discuss in Section 8-4. Before we do so, let’s look at the relation of the Phillips curve to the concept of the natural rate of unemployment we derived in Chapter 7.

8-3 The Phillips Curve and the Natural Rate